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Existence of Solutions to Some Equilibrium Problems

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Abstract

The concept of a monotone family of functions, which need not be countable, and the solution of an equilibrium problem associated with the family are introduced. A fixed-point theorem is applied to prove the existence of solutions to the problem.

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References

  1. T. Husain E. Tarafdar (1994) ArticleTitleSimultaneous Variational Inequalities, Minimization Problems, and Related Results Mathematica Japonica. 39 221–231

    Google Scholar 

  2. T. Husain E. Tarafdar (1996) ArticleTitleCorrigendum to: Simultaneous Variational Inequalities, Minimization Problems, and Related Results Mathematica Japonica. 43 175

    Google Scholar 

  3. E. Tarafdar (1987) ArticleTitleA Fixed-Point Theorem Equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz Theorem Journal of Mathematical Analysis and Applications. 128 475–479 Occurrence Handle10.1016/0022-247X(87)90198-3

    Article  Google Scholar 

  4. Djafari Rouhani B.,. Tarafdar E., Watson J. (2001). Fixed-Point Theorems, Coincidence Theorems, and Variational Inequalities, Proceedings of the 6th International Symposium on Generalized Convexity/Monotonicity, Samos, Greece, 1999, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, Germany. 502: 183–188,

  5. L.J. Lin Z.T. Yu (2001) ArticleTitleFixed-Point Theorems and Equilibrium Problems Nonlinear Analysis. 43 987–999 Occurrence Handle10.1016/S0362-546X(99)00202-3

    Article  Google Scholar 

  6. Q.H. Ansari J.C. Yao (1999) ArticleTitleA Fixed-Point Theorem and Its Application to the System of Variational Inequalities Bulletin of the Australian Mathematical Society. 59 433–442

    Google Scholar 

  7. M. Bianchi N. . Hadjisavvas S. Schaible (1997) ArticleTitleVector Equilibrium Problems with Generalized Monotone Bifunctions Journal of Optimization Theory and Applications. 92 527–542 Occurrence Handle10.1023/A:1022603406244

    Article  Google Scholar 

  8. G. Cohen F. Chaplais (1988) ArticleTitleNested Monotonicity for Variational Inequalities over Product of Spaces and Convergence of Iterative Algorithms Journal of Optimization Theory and Applications. 59 369–390 Occurrence Handle10.1007/BF00940305

    Article  Google Scholar 

  9. J.S. Pang (1985) ArticleTitleAsymmetric Variational Inequality Problems over Product Sets: Applications and Iterative Methods Mathematical Programming. 31 206–219

    Google Scholar 

  10. E. Tarafdar (1990) ArticleTitleNonlinear Variational Inequality with Application to the Boundary-Value Problem for Quasilinear Operators in Generalized Divergence Form Funkcialaj Ekvacioj. 33 441–453

    Google Scholar 

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Author information

Authors and Affiliations

  1. Professor, Institute for Studies in Nonlinear Analysis School of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran, Iran

    B. Djafari. Rouhani

  2. Associate Professor, Department of Mathematics, University of Queensland, Queensland, Australia

    E. Tarafdar

  3. Researcher, IKOS Research, Brighton, UK

    P. J. Watson

Authors
  1. B. Djafari. Rouhani
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  2. E. Tarafdar
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  3. P. J. Watson
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Additional information

1The authors are thankful to the referees and Professor S. Schaible for valuable suggestions and comments to make the paper in the present form. The first author thanks the Department of Mathematics, University of Queensland for the kind hospitality shown during his stay 2This research was supported in part by grant No. 83470019 from IPM

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Rouhani, B.D., Tarafdar, E. & Watson, P.J. Existence of Solutions to Some Equilibrium Problems. J Optim Theory Appl 126, 97–107 (2005). https://doi.org/10.1007/s10957-005-2660-7

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  • DOI: https://doi.org/10.1007/s10957-005-2660-7

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